I checked with MFA yesterday. They said that Ministry of Health (MOH) has advised that thus far, there have been no reported cases of Singaporeans with radiation illness due to travels to Japan. The current radiation levels in Tokyo are within international acceptable limits, and close to Singapore's level. If you have any health concerns, you may wish to consult Travellers Clinic at Tan Tock Seng Hospital and take the necessary precautions. So probably these rumours are unreal.